Copyright 2001 American Physical Society. The following article appeared in Physical Review A, 64:3; http://pra.aps.org/abstract/PRA/v64/i3/e032310

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Abstract: Entanglement is the fundamental quantum property behind the now popular field of quantum transport of information. This quantum property is incompatible with the separation of a single system into two uncorrelated subsystems. Consequently, it does not require the use of an additive form of entropy. The authors discuss the problem of the choice of the most convenient entropy indicator, focusing their attention on a system of two qubits, and on a special set, denoted by ℑ. This set contains both the maximally and partially entangled states that are described by density matrices diagonal in the Bell basis set. The authors select this set for the main purpose of making their work of analysis more straightforward. As a matter of fact, the authors find that in general the conventional von Neumann entropy is not a monotonic function of the entanglement strength. This means that the von Neumann entropy is not a reliable indicator of the departure from the condition of maximum entanglement. The authors study the behavior of a form of nonadditive entropy, made popular by the 1988 work by Tsallis [J. Stat. Phys. 52, 479 (1988)]. The authors show that in the set ℑ, implying the key condition of nonvanishing entanglement, this nonadditive entropy indicator turns out to be a strictly monotonic function of the strength of the entanglement, if entropy indexes q larger than a critical value Q are adopted. The authors argue that this might be a consequence of the nonadditive nature of the Tsallis entropy, implying that the world is quantum and that uncorrelated subsystems do not exist.